How do you factor the trinomial #x² - 7x + 12#?

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Answer 1 · 2015-12-23T17:12:23

#color(blue)((x -4) (x-3)# is the factorised form of the expression.

#x^2-7x+12#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*12 =12#

AND

#N_1 +N_2 = b = -7#

After trying out a few numbers we get #N_1 = -3# and #N_2 =-4#
#-3*-4 = 12#, and #(-3)+(-4)= -7#

#x^2color(blue)(-7x)+12 = x^2color(blue)(-3x-4x)+12#

#=x (x-3) -4(x-3)#

#color(blue)((x -4) (x-3)# is the factorised form of the expression.